Drain the pumpkin well, cut into small pieces. Peel and coarsely grate the potatoes, then mix with the pumpkin. Mix with eggs and flour and season with salt, pepper and nutmeg.
Heat the oil in a pan and add the rösti mixture, tablespoon at a time, press a little until smooth and fry for about 5 minutes on each side.
For the dill pickles, halve, core and dice the cucumber. Finely chop the onion, stir into the yogurt with the cucumber and dill. Season to taste with salt and pepper.
Cut the chives into rings. Turn the salmon into florets and arrange on plates with the hash browns. Röstis with a dollop of sour cream, sprinkled with chives, serve with the dill pickles.